Bridging the gap between accurate ab initio many-body theory and simple density-functionals

密度泛函理论处于当今量子力学方法的前沿，用于描述分子和材料，这些分子和材料是各种技术的基石。该方法预测能力和准确性的关键是对电子的量子力学交换和关联相互作用的处理。目前对这些贡献的近似值仅限于狭窄的适用范围--本提案中的工作将开发新的近似值，以显著扩大可行的应用范围。描述能量交换和关联贡献的方法往往是基于电子密度分布及其梯度的相对简单的模型。使用基于多电子波函数的第一性原理技术可以获得更高的精度。在这项工作中，我们构建了一个通用框架，用于比较这些昂贵的高精度方法与简单的密度泛函近似。这一框架为新的简单模型的发展提供了新的见解--特别是强调了密度的更高导数作为描述电子关联的关键变量。在这项工作中将开发基于这个量的泛函，为更准确和更稳健的相关处理开辟道路-消除困扰目前近似的误差抵消。

Density-functional theory is at the forefront of today's quantum mechanical approaches for the description of the molecules and materials that are the building blocks for a diverse range of technologies. The key to the predictive power and accuracy of the approach is the treatment of the quantum mechanical exchange and correlation interactions of the electrons. Present-day approximations for these contributions are limited to a narrow comfort zone of applicability - the work in this proposal will develop new approximations to significantly expand the range of viable applications. Methods to describe the exchange and correlation contributions to the energy are often relatively simple models based on the electronic density distribution and its gradient. Higher accuracy can be obtained using first-principles techniques based on the many-electron wave function. In this work we construct a common framework for the comparison of these expensive high accuracy approaches with simple density-functional approximations. This framework gives new insight into the development of new simple models - in particular the higher derivatives of the density are highlighted as a key variables for the description of electronic correlation. Functionals based on this quantity will be developed in this work, opening the way to more accurate and robust correlation treatments - removing error cancellations that plague present-day approximations.